AMC 8 2019 Problem 1

AMC8 2019 年第 1 题

表达式与运算★☆☆☆☆

Ike and Mike go into a sandwich shop with a total of $30.00 to spend. Sandwiches cost $4.50 each and soft drinks cost $1.00 each. Ike and Mike plan to buy as many sandwiches as they can, and use any remaining money to buy soft drinks. Counting both sandwiches and soft drinks, how many items will they buy?

Ike 和 Mike 带着总共 30 美元去一家三明治商店，每块三明治价格 4.5 美元，每瓶软饮价格 1 美元。Ike 和 Mike 打算尽可能多的买三明治，然后用剩下的钱去买软饮料，那么三明治和软饮总个数加起来，他们将买多少件物品？

A.6
B.7
C.8
D.9
E.10

正确答案 · Correct Answer

解析 · Solution

Solution 1

We know that the sandwiches cost 4.50 dollars. Guessing will bring us to multiplying 4.50 by 6, which gives us $27.00$. Since they can spend $30.00$, they have 3 dollars left. Since soft drinks cost 1.00 dollar each, they can buy 3 soft drinks. Since they bought 6 sandwiches and 3 soft drinks, they bought a total of 9 items. Therefore, the answer is 9.

Let

s

be the number of sandwiches and

d

be the number of sodas. We have to satisfy the equation 4.50s+d=30 In the question, it states that Ike and Mike buy as many sandwiches as possible. So, we drop the number of sodas for a while. We have $$$$

\displaystyle \begin{aligned} 4.50s&=30 \\ s&= \frac{30}{4.5} \\ s&=6R3 \end{aligned}

$$$$ We don't want a remainder, so the maximum number of sandwiches is 6. The total money spent is

6\cdot 4.50=27

. The number of dollars left to spend on sodas is 30-27=3 dollars. 3 dollars can buy 3 sodas, leading us to a total of 6+3=9 items. Hence, the answer is 9.

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